Question: Ming throws a stone off a bridge into a river below. The stone's height (in meters above the water), $x$ seconds after Ming threw it, is modeled by: $h(x)=-5(x-1)^2+45$ What is the maximum height that the stone will reach?
The stone's height is modeled by a quadratic function, whose graph is a parabola. The maximum height is reached at the vertex. So in order to find the maximum height, we need to find the vertex's $y$ -coordinate. The function $h(x)$ is given in vertex form. The vertex of $-5(x-{1})^2{+45}$ is at $({1},{45})$. In conclusion, the maximum height that the stone will reach is $45$ meters.